In an interesting paper titled, 'Decagonal and
Quasi-Crystalline Tilings in Medieval Islamic Architecture', authored by Peter
J. Lu, et al, Science 315, 1106 (2007) it has been convincingly argued
that by the 1200 A.D. Islamic mathematicians had made a breakthrough in geometry
that made it possible to create extraordinary complex patterns having a 10-fold
rotational symmetry. A set of five tile types, now called Ďgirih tilesí, in any
combinations serve as templates for tessellation with patterns incorporating
decagonal symmetry.

This advance in use of mathematics in architecture was
impressively exploited in decorating Islamic buildings constructed in 15th
and 16th centuries in Afghanistan, Iran, India and Turkey. Tilings
expressing complex decagonal motif based on tessellation with three types of
girih tiles can be seen in the monument at Agra known as 'Iítmad-Ud-Daula'. It
was built in 1611 by Nur Jehan, wife of Mughal emperor Jehangir, as a mausoleum
of her parents. I made a visit to Agra to see this monument. I was rewarded much
beyond my expectations when I saw this beautiful monument, which French visitors
have appropriately called petite Taj. I am happy to share with the users of the
web a pictorial album of Iítmad-Ud-Daula with a fond hope that perhaps visitors
who come to Agra to see the Taj Mahal may plan to include in their itinerary a
visit to this extraordinarily beautiful monument.

I'tmad-Ud-Daulah is the tomb of Mirza Ghiyas Beg and his wife
Asmat Begum. He hailed from Iran and served Akbar. He was father of the famous 'Nur-Jehan'
and grandfather of 'Mumtaz-Mahal' of the famous Taj Mahal fame. He was made
Vazir (Prime Minister) after Nur Jehan's marriage with Jehangir in 1611. He held
the title I'tmad-Ud-Daulah (The Lord Treasurer). He died at Agra in 1622, a few
months after his wife's death. Nur Jehan built this tomb for her parents between
1622 and 1628. Her own tomb and that of Jehangir are at Lahore.

The tomb is situated on the Eastern bank of the river Yamuna
at Agra. It is located in the centre of a char-bagh (four quartered
garden), with the usual enclosing walls and side buildings. Its main gate is on
the Eastern side. Ornamental gateways with prominent lawns are built in the
middle of North and South sides. A multi-storeyed open pavilion on the Western
side overlooks the river impressively. The outer buildings are of red stone with
inlaid designs in white marble.

Shallow water channels, sunk in the middle of the raised
stone pathways, with intermittent tanks and cascades, divide the garden into
four equal quarters. They are only slightly raised from the parterres which
could be converted into flower beds. Space for large plants and trees was
reserved just adjoining the enclosing walls, leaving the mausoleum open to view.

The most important aspect of this tomb is its polychrome
ornamentation. Exterior walls of the tomb have been covered with beautiful
floral and geometrical designs have. Inside the oblong rooms using pleasing
tints and tones wall paintings were made of wine-vases, flower vases, and such
other Iranian motifs, typical of the art of Jahangir. By far, it is the most
gorgeously ornamented Mughal building. It testifies that 'Mughals began like
titans and finished like jewellers'.

The tomb of I'tmad-Ud-Daulah is a masterpiece of dome-less class
of Mughal tombs. It is made in white marble and marks transitional phase from
red stone to white marble, from the Akbar's tomb, Sikandara, to the Taj Mahal.

A modest attempt to draw manually a pattern with 10-fold rotational
symmetry using in combination decagonal, hexagonal and bow girih tiles is shown
below.

The same pattern has been redrawn using computer
for colour selection of tiles and obtaining a line sketch. We show them below